we had to move a 3200 lb diesel generator. SO it was on 6 legs, I measured the square legs, and make a plate with 4 sides so it cupped the units legs, and then put 4 casters on each plate. We went there with air powered bottle jacks, jacked it up just enough to lower it onto the plate I made. There was a hole in each square foot so while on the sight I figured drill my plate and bolt the wheels on, not that it was going anywhere BUT, safe is better than sorry and we had to wait for the trailer to get their anyway...
The trailer go there and we pushed that thing right to it (on cement), I could have pushed it alone, it moved like a shopping carriage (a bit harder to stop though, lol)...
And the bolting the plates on worked out great because when we picked it up with the machine after it was outside the building they stayed right on there....
A fork lift is normally the best bet for anything like this, they are also normally designed to be lifted by forks. I have a small wheel electric forklift that lifts 5000lbs, the trick is stay low, and come along chain it down if you are going over anything unlevel, or it is an off center top heavy load...